Muchodeportivo are reporting that Spurs have agreed terms with Olmo's agent and a deal could be done for €25 million.
Olmo was part of Spain's Under-21 European Championship-winning side.
The 21-year-old cut his teeth at Barcelona's famed La Masia academy before joining Dinamo Zagreb as a youngster in 2015.
In what was his breakout season last year, he scored 12 goals and assisted nine more.
Spurs are believed to want reinforcements in midifield after their club record capture of Tanguy Ndombele from Lyon.
Olmo would help plug any hole left in attacking midfield by Christian Eriksen, who could be leaving north London this summer.
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